Positive solutions for the Robin ▫$p$▫-Laplacian plus an indefinite potential

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

We consider a nonlinear elliptic equation driven by the Robin ▫$p$▫-Laplacian plus an indefinite potential. In the reaction we have the competing effects of a strictly ▫$(p-1)$▫-sublinear parametric term and of a ▫$(p-1)$▫-linear and nonuniformly nonresonant term. We study the set of positive solutions as the parameter ▫$\lambda > 0$▫ varies. We prove a bifurcation-type result for large values of the positive parameter ▫$\lambda$▫. Also, we show that for all admissible ▫$\lambda > 0$▫, the problem has a smallest positive solution ▫$\overline{u}_\lambda$▫ and we study the monotonicity and continuity properties of the map ▫$\lambda \mapsto \overline{u}_\lambda$▫.

• Language: English
• Keywords: local minimizers, p-Laplacian, strong comparison, positive solutions, nonlinear regularity, minimal solution, indefinite potential
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: Str. 1217-1236
• Numbering: Vol. 5, no. 15
• PID: 20.500.12556/RUL-121493
• UDC: 517.956
• ISSN on article: 2189-3756
• COBISS.SI-ID: 32039427
• Publication date in RUL: 12.10.2020

Record is a part of a journal

• Title: Pure and applied functional analysis
• Shortened title: Pure appl. funct. anal.
• Publisher: Yokohama Publishers
• ISSN: 2189-3756
• COBISS.SI-ID: 18455385